Question

I was struggling with this statistics problem:

Suppose a research team takes a simple random sample of 100 Parma wallabies. In this sample, the tails of the wallabies have a mean length of 46 centimeters and a standard deviation of 2.6 centimeters.

What percent of the time would you expect a simple random sample of 100 Parma wallabies to have a sample mean that is not in the 95% confidence interval?

5%
0%
2.5%
5%

Answer 1

I think your answer would be 5%.

Answer 2

5%

Explanation:

Given that a research team takes a simple random sample of 100 Parma wallabies. In this sample, the tails of the wallabies have a mean length of 46 centimeters and a standard deviation of 2.6 centimeters

When confidence interval is calculated for 95% we expect approximately 95% of sample mean will be within this interval for large sample sizes.

Hence Per cent of the time you would expect a simple random sample of 100 Parma wallabies to have a sample mean that is not in the 95% confidence interval=100%-95% =5%